Adaptive Sagnac interferometer with dynamic population grating in saturable rare-earth-doped fiber

Jorge López Rivera; Marcos Plata Sánchez; Alexei Miridonov; Serguei Stepanov

doi:10.1364/OE.21.004280

1. Introduction

Dynamic population Bragg gratings in the rare-earth-doped (Er, Yb, etc.) optical fibers are recorded by two counter-propagating coherent light waves [1,2]. The optical absorption/gain of the fiber is effectively saturated in the bright fringes of the interference pattern leading to the formation of the amplitude Bragg grating. This spatially periodic change of the fiber absorption/gain is inevitably accompanied by a corresponding change of the fiber refractive index, which leads to formation of the phase Bragg grating. Typically [2] such dynamic fiber gratings need near-IR cw laser power of the milli-Watt scale for their formation and are characterized by the millisecond/sub-millisecond recording/erasure time τ. These gratings were found to be promising for applications in tunable narrow-band optical filters [3,4], in single-frequency fiber lasers [5–7], and in interferometric optical fiber sensors for adaptive detection of the light phase modulation [8].

Generally, in the above-mentioned adaptive interferometric sensors, the dynamic grating (in particular, the photorefractive one) is utilized as an “intelligent” beam-splitter that permanently compensates for slow environmentally induced phase shifts in the recording waves [9,10]. This keeps the interferometer operation point fixed and the interferometer itself permanently ready for an optimal detection of the information bearing phase modulation of a higher frequency Ω > τ⁻¹. The highest sensitivity of the interferometric detection configurations (and in particular, of those based on the dynamic gratings [11]) is limited by the fundamental photon noise.

Our earlier reported experiments [8] demonstrated that practical sensitivity of the rare-earth doped fiber adaptive interferometric configurations is limited by multiple spurious reflections among different elements of the fiber arrangement, which interfere in a random way at the photodetector and increase the noise. Below in this paper we propose a simple closed-loop Sagnac adaptive fiber configuration which is characterized by minimal reflections inside the interferometer loop. We investigate characteristic features of this original adaptive configuration and demonstrate its practical applicability with detection of vibrations in the frequency range 200-2000 Hz.

2. Operation principle

The schematic of the arrangement is shown in Fig. 1(a) . The closed optical fiber loop is formed by the fiber coupler FC1 with the division ratio r/(1 - r) and the doped fiber segment which is spliced between the output terminals of this coupler (“3” and “4”). The main output signal is detected in the transmitted light wave at the entrance terminal “2” of the FC1. Additional output signal is also detected in the wave reflected from the loop to the entrance terminal “1”.

Fig. 1 Schematic of the adaptive fiber Sagnac configuration - a, and the reflection and transmission coefficients of the conventional configuration (i.e. without dynamic grating) as functions of the division ratio of the input coupler – b

Download Full Size | PDF

In conventional (i.e. without doped fiber) Sagnac fiber configuration [12], because of an additional π/2 phase shift in the light wave reflected from the fiber coupler, the transmitted through the Sagnac interferometer output wave is formed as a result of the destructive interference of the waves S1 (with the normalized power r) and S2 (with the normalized power 1 - r), which reenter the output terminals (“3” and “4” – see Fig. 1(a)) of coupler FC1. This results, in particular, in a complete disappearance of the transmitted light power (i.e. that detected at terminal “2”) in case of r = 0.5. In a general case, the transmission intensity coefficient of the configuration equals:

T = {| \sqrt{r} \sqrt{r} - \sqrt{1 - r} \sqrt{1 - r} |}^{2} = {(2 r - 1)}^{2} .

On the opposite, the reflected from the Sagnac loop light wave is formed as a result of the constructive interference of the same waves S1 and S2 and the reflection intensity coefficient equals:

R = {| \sqrt{1 - r} \sqrt{r} + \sqrt{r} \sqrt{1 - r} |}^{2} = 4 r (1 - r) = 1 - T .

The conventional light attenuation inside the Sagnac loop (which was neglected in the above consideration) results in proportional reduction of the transmitted and the reflected light power.

When the saturable rare-earth doped fiber is introduced in the loop, the two above-mentioned waves S1 and S2 counter-propagating in the Sagnac loop form the dynamic population Bragg grating [1,2] inside the doped fiber segment. As a result of the self-diffraction of these two recording waves from this Bragg grating two additional waves R1 and R2 appear inside the Sagnac loop – see Fig. 1(a). It is expected that the appearance of these waves and their interference with the initial waves recording the grating (i.e. the effect which is known as a two-wave-mixing or TWM) have to change the light power at the outputs of the Sagnac configuration (i.e. at terminal “2” and “1”). Below we show that the result depends on the type (amplitude or/and phase) of the dynamic grating formed in the saturable fiber. Note that, for the symmetry reasons, the recorded dynamic Bragg grating is always of the un-shifted type, i.e. the maxima (or the minima) of the recorded absorption (or refractive index) profile coincide with the corresponding maxima of the recording interference pattern.

The main results can be easily obtained in approximation of low diffraction efficiency (η << 1) of the recorded Bragg grating. In this case one can neglect the general attenuation of the light waves transmitted through the doped fiber and accept that the weak diffracted waves R1 and R2 have the normalized powers ηr and η(1 – r) respectively. Phasing of the diffracted waves with the collinearly propagating recording waves S2 and S1 is of a crucial importance and depends on the type of the recording dynamic grating.

Without performing a formal detailed analysis for a general case we start with consideration of the simplest case of the amplitude grating recorded in the doped fiber with the saturable absorption (i.e. that without optical pumping). As it was shown earlier (see e.g [2,13].), in this case both diffracted waves R1 and R2 prove to be in phase with the collinearly propagating recording waves S2 and S1. The transmission and reflection coefficients of the configuration (see Eq. (1), (2)) are transformed for this case in the following way:

T = T_{l} {| \sqrt{r} (\sqrt{r} + \sqrt{η} \sqrt{1 - r}) - \sqrt{1 - r} (\sqrt{1 - r} + \sqrt{η} \sqrt{r}) |}^{2} = T_{l} {(2 r - 1)}^{2} .

\begin{array}{l} R = T_{l} {| \sqrt{1 - r} (\sqrt{r} + \sqrt{η} \sqrt{1 - r}) + \sqrt{r} (\sqrt{1 - r} + \sqrt{η} \sqrt{r}) |}^{2} \approx \\ T_{l} [4 r (1 - r) + 4 \sqrt{η} \sqrt{r} \sqrt{1 - r}] . \end{array}

Here

T_{l}

(< 1) is the transmission coefficient for one round-trip through the Sagnac loop associated with the average absorption of the doped fiber. In the above equations, we have also neglected the smaller terms linear on η (<< 1).

From the presented above formulas one can see that in the steady-state the recorded amplitude dynamic grating increases the reflected from the Sagnac loop light power only. Because of the above-mentioned destructive nature of the interference of the waves counter-propagating inside the Sagnac loop similar increase in the transmitted wave is not observed.

Let us introduce periodic phase modulation in one of the segments of the fiber loop between the coupler PC1 and the doped fiber – see Fig. 1. For simplicity of consideration, we assume that this modulation is of a small amplitude Δ << 1 rad and has rather high frequency Ω >> τ⁻¹ where τ is the dynamic grating recording time. Under such conditions we can neglect the influence of the interference pattern vibrations on the grating recording, consider that it is stable (i.e. it is not vibrating), and has its maximum stationary diffraction efficiency η. The phase modulation is described by the following multiplicative factor:

exp (i Δ \sin Ω t),

which is to be applied to the complex amplitudes of all waves passing through the modulation area.

From Fig. 1 one can see that before leaving the Sagnac loop the transmitted waves S1 and S2 go one time through the modulation area, the diffracted wave R1 obtains the double modulation, while the diffracted wave R2 has no periodic modulation at all. In our consideration of the output intensities we can neglect the general phase modulation $exp (i Δ \sin Ω t)$ in all the waves and assume that the transmitted waves S1 and S2 gets no modulation, R1 obtains modulation $exp (i Δ \sin Ω t)$ and R2 obtained the inverted modulation $exp (i Δ \sin Ω t)$ . In this case, the above Eqs. (3), (4) for the transmission and reflection intensity coefficients change in the following way:

\begin{array}{l} T = T_{l} {| \sqrt{r} [\sqrt{r} + \exp (- i Δ \sin Ω t) \sqrt{η} \sqrt{1 - r}] - \sqrt{1 - r} [\sqrt{1 - r} + \exp (i Δ \sin Ω t) \sqrt{η} \sqrt{r}] |}^{2} = \\ T_{l} {| (2 r - 1) - 2 i \sin (Δ \sin Ω t) \sqrt{r} \sqrt{η} \sqrt{1 - r} |}^{2} \approx T_{l} (^{2 r - 1) 2}, \end{array}

\begin{array}{l} R = T_{l} {[\sqrt{1 - r} (\sqrt{r} + \exp (- i Δ \sin Ω t) \sqrt{η} \sqrt{1 - r}) + \sqrt{r} (\sqrt{1 - r} + \exp (i Δ \sin Ω t) \sqrt{η} \sqrt{r})]}^{2} = \\ T_{l} {[2 \sqrt{r} \sqrt{1 - r} + i (2 r - 1) \sqrt{η} \sin (Δ \sin Ω t) + \sqrt{η} \cos (Δ \sin Ω t)]}^{2} \approx \\ T_{l} {4 r (1 - r) + 4 \sqrt{n} \sqrt{r} \sqrt{1 - r} [1 + \frac{{(Δ \sin Ω t)}^{2}}{2}]} . \end{array}

In the above equations, we have also neglected the smaller terms linear on η (<< 1). From here we can see that the result of the periodic phase modulation appears only in the reflected wave in the form of a second harmonic intensity modulation. In general, the second harmonic of modulation can also appear in the transmitted wave, but with significantly lower amplitude proportional to η only.

In case of a purely phase un-shifted dynamic grating, both diffracted waves obtain additional ± π/2 phase shift depending on the sign of the refractive index modulation [11,12,14]. In the above equations for the reflection/transmission coefficients this allows us to substitute $\sqrt{η}$ by $i \sqrt{η}$ , which results in:

\begin{array}{l} T = T_{l} {| (2 r - 1) + 2 \sin (Δ \sin Ω t) \sqrt{r} \sqrt{η} \sqrt{1 - r} |}^{2} \approx \\ T_{l} | {(2 r - 1)}^{2} + 4 \sqrt{η} Δ \sin Ω t (2 r - 1) \sqrt{r} \sqrt{1 - r} |, \end{array}

\begin{array}{l} R = T_{l} {| 2 \sqrt{r} \sqrt{1 - r} - (2 r - 1) \sqrt{η} \sin (Δ \sin Ω t) + i \sqrt{η} \cos (Δ \sin Ω t) |}^{2} \approx \\ T_{l} {[4 r (1 - r)] - 4 \sqrt{η} Δ \sin Ω t (2 r - 1) \sqrt{r} \sqrt{1 - r}} . \end{array}

The TWM response is, clearly, linear one in this case (i.e., at the first harmonic of the modulation frequency) and with the amplitude proportional to

\sqrt{η}

. Additionally, we can see that the sum of the periodically oscillating components in the transmitted and reflected wave powers is equal to 0, i.e. they oscillate in anti-phase. That means that, as expected for the phase grating, we observe an energy exchange between these two output waves.

The presented analysis shows, in particular, that to have a strong linear response in this configuration the dynamic grating needs a significant contribution of the phase (i.e refractive index) component. The amplitude grating has no significant influence on the transmitted output signal.

3. Experimental results

In the below-presented experiments we utilized single-mode erbium doped fiber (EDF) HG980 (purchased from the “OFS-Fitel”) operated at the wavelength 1485 nm of the 20 mW distributed feedback CW semiconductor InGaAlAs laser. This wavelength was selected because of a significant contribution of the phase component in the recorded dynamic grating [14]. Indeed, the phase (i.e. refractive index) gratings in EDF are rather inefficient when they are recorded in the spectral region (around 1550 nm) of a minimal dispersion of conventional silica fibers. The 1.9 m long EDF piece was spliced between the output terminals of the 30/70 input fiber coupler (FC1 in Fig. 2(a) ). This ensured approximately symmetric position of the doped fiber segment (and of the recorded dynamic grating) inside the Sagnac loop. The initial (not saturated) optical density α₀L of the doped fiber at the operation wavelength was evaluated to be ≈1.8.

Fig. 2 The real set up utilized in the experiments – a (inset shows how the phase modulation is introduced via piezo-electric modulator PZ and the inertial mass m), and the experimentally measured average output (transmitted) light power as a function of the incident light power – b.

Download Full Size | PDF

The optical fiber Sagnac loop was connected to the laser via 10/90 fiber coupler FC2, which was also utilized to monitor the incident laser power via photodiode PD2 – see Fig. 2(a). The incident power was controlled by the variable attenuator (AT) and the polarization controller (PC) was used to adjust the input light polarization. The fiber isolator (IS) was utilized to prevent back-reflections to the laser. The division ratios of both fiber couplers were selected in this way to have approximately equal average output powers in the transmitted (detected via PD1) and the reflected (detected via PD3) from the Sagnac loop waves. To prevent undesirable spurious reflections inside the configuration all the fiber elements were spliced and the APC connectors were utilized at all free terminals of both couplers connected to the photodiodes.

Additional direct measurements of the growth rate of the transversally detected fluorescence which was excited by the periodically modulated power of the DFB laser (see e.g [15].) have shown that the saturation power of the doped fiber is about 0.5 mW at the operation wavelength. Indeed, a significant saturation of the average transmitted power was clearly observed in the milli-Watt range of the incident power – see Fig. 2(b). It is manifested in a significant deviation of the output power from the linear approximation of the dependence observed at low incident power which is shown in the figure by the lower dashed line.

The periodic phase modulation was introduced in the Sagnac loop by periodic stretching the short segment of one output tail of the input fiber coupler FC1. In this modulation element, one end of this fiber segment was attached to the piezoelectric transducer and the inertial mass m was hanged to its other end – see inset to Fig. 2(a). In fact, we have reproduced the configuration which was proposed earlier in [16] as an optical fiber accelerometers.

Typical shapes of the signals detected in the transmitted and reflected output light waves in response to a sinusoidal modulation are shown in Figs. 3(a) -3(d). Modulation amplitude dependences of the first and the second harmonic components in the transmitted and reflected waves measured via lock-in amplifier are presented in Fig. 4 . These dependences clearly demonstrate significantly larger distortions associated with presence of the second harmonics of modulation frequency in the reflected wave.

Fig. 3 Typical shapes of the signals detected in the transmitted (a) and reflected (b) waves at a moderate sinusoidal modulation amplitude 3 Vp-p, (c) and (d) are the same signals but observed at relatively large modulation amplitude 10 Vp-p (modulation frequency – 700 Hz, input light power – 0.9 mW).

Download Full Size | PDF

Fig. 4 Experimental dependencies of the normalized amplitude of the fundamental (◼) and the second (⬤) harmonic component in the transmitted (a) and reflected (b) waves (modulation frequency – 700 Hz, input light power – 0.9 mW). Dashed lines correspond to the linear and quadratic dependences expected in low modulation approximation from these two dependences.

Download Full Size | PDF

As it was shown in [16], the segment of the fiber with the attached inertial mass represents rather complicated oscillator system, which, in general, demonstrates different resonances (stretching, oscillating, torsional). In our experiments, to reduce the resonance frequencies and to move them to the frequency band below 100-200 Hz we utilized a rather heavy mass m ≈50 g and the stretched fiber segment of 2.5 cm length. Typical spectral curve of the response amplitude obtained with the network analyzer SR770 is presented in Fig. 5 . One can see that above the fundamental resonance around 150 Hz the response curve is nearly flat. Rather fast decay of the response amplitude below this resonance is also governed by the response time τ of the recorded dynamic grating, which is usually [2] somewhat below the spontaneous relaxation time τ₀ ≈10 ms of the Er³⁺ ion meta-stable state [17]. For the modulation frequencies above the resonance we can assume that the inertial mass is practically stable (i.e. it is not moving), and the fiber segment is stretched following the displacement introduced by the piezoelectric transducer. Note that our interest in operation of the device above the resonance frequency was basically determined by the special purpose of this optical fiber sensor for detection of the ground vibration signals in the frequency range 200 – 1000 Hz. By simple reduction of the inertial mass [16] one can switch it for operation below the resonance frequency that is more typical for conventional accelerometers.

Fig. 5 Frequency transfer function (i.e. dependence of the output signal amplitude on the modulation frequency) of the Sagnac adaptive configuration (input light power – 0.9 mW, low amplitude modulation, stretched fiber segment length – 2.5 cm, inertial mass – 50 g).

Download Full Size | PDF

An adequate selection of the recording light power is an issue of a great importance in the systems based on dynamic population gratings [2]. Usually, the most profound modulation of the output light power is observed when the total incident recording power is somewhat above the saturation power of the doped fiber [15]. Indeed, the lower recording light power does not saturate the fiber and does not result in an effective formation of the grating. On the opposite, significantly larger recording power saturates the fiber too much, which also prevents from formation of an efficient grating. Figure 6 represents the dependence of the modulation depth in the detected transmitted signal as a function of the total light power incident at the configuration. One can see that the maximum modulation depth around 25-30% in the transmitted signal is reached for the incident power about 1.1 mW.

Fig. 6 Input light power dependence of the normalized output signal amplitude at the fundamental harmonic of modulation (modulation frequency – 700 Hz, modulation voltage – 2.5 Vp-p).

Download Full Size | PDF

In conclusion to this section we present the frequency spectra of the transmitted output signal obtained at optimum incident light power under different experimental conditions. In particular, Fig. 7(a) presents the spectrum of the output electronic noise observed with the laser source switched off. Figure 7(b) shows similar output noise with the laser on, without external modulation and without inertial mass attached to the fiber. We assume that without the inertial mass the sensitivity of the configuration to the environmental vibrations is reduced significantly, and this allows us to observe basically the optical noise of our interferometer. Figure 7(c) shows the similar noise signal observed, however, with the attached mass.

Fig. 7 Frequency spectra of the output signal detected in transmitted wave: a – with the laser turned-off, b – with the laser turned-on but without inertial mass, c – the same with inertial mass, and d – the same with applied modulation voltage 6 Vp-p of 700 Hz (incident light power – 0.9 mW).

Download Full Size | PDF

Some additional noise maxima (especially at low frequencies) are observed here, which we can attribute to the environmental vibrations in the laboratory building. Finally, Fig. 7(d) shows the output spectrum detected when the external modulation voltage of 6 Vp-p, resulting in a maximum output signal (see Fig. 4), is applied to the piezoelectric transducer.

Comparison of this maximal output signal amplitude with the optical noise level at the same frequency allows us to evaluate the maximal signal-to-noise ratio or the minimal detectable phase modulation amplitude for our adaptive detection configuration. In this evaluation we take into account that the noise curve presented in Fig. 7(b) was obtained with SR770 spectrum analyzer for ≈2.5 Hz frequency band. As a result, the noise density at typical frequency 700 Hz is about 3 × 10⁻⁵/2.5^1/2 ≈2 × 10⁻⁵ V/Hz^1/2. Also, the maximum linearized value of the signal observed at 1 rad amplitude of phase modulation can be obtained by multiplication of the maximum signal presented in Fig. 7(d) by factor ≈1.5 (reduction in the dynamic grating amplitude - see Fig. 4) and equals ≈0.5 V. The ratio between these two values gives us the detection resolution (i.e. minimal detected amplitude) ≈4*10⁻⁵ rad/Hz^1/2.

If we use this figure to evaluate the resolution of configuration for detection of accelerations, for modulation frequency 200 Hz we get the value about 1.0 μg/Hz^1/2, which is close to the minimal detectable acceleration (≈0.5 μg) reported in [16] for the same frequency. Note that unlike this earlier reported configuration, our arrangement does not need external optoelectronic loop for an active stabilization of the interferometer operation point.

4. Discussion

As one can see from the above-presented experimental results, the investigated Sagnac configuration demonstrates the main characteristic features predicted by our theoretical analysis. Indeed, the fundamental modulation frequency component is present in both output waves (reflected and transmitted) and is in anti-phase, which is typical for an energy exchange via two-wave mixing at the un-shifted phase grating. The quadratic response from the amplitude grating component is essentially weaker at moderate modulation amplitudes and appears basically in the reflected wave at strong modulation. As expected, the maximum normalized output signals are observed for milli-Watt incident light power, which is close to the saturation power of the utilized EDF at the operation wavelength.

Essentially similar results were also observed for a similar Sagnac configuration based on the ytterbium-doped fiber (YDF) with the operation wavelength 1064 nm. The dynamic population grating in this fiber is basically of a phase type [18], which results in a linear response of the adaptive interferometric configuration both in the transmitted and reflected waves. The main difference with EDF is that the spontaneous relaxation time of the meta-stable state of Yb³⁺ is nearly ten times shorter (τ₀ ≈1 ms) than in EDF, for this reason the dynamic gratings are recorded nearly ten times faster. For the same reason, the YDF based configurations need approximately ten times larger input light power for their operation. The maximal resolution of the device based on YDF proved to be very close to that mentioned above for that based on EDF.

The main characteristics which needs more detailed discussion is the sensitivity of the adaptive detection configurations in question. As it was mentioned in the above section, for the average detected power 0.02 mW, the ratio between the noise density and the detected signal average level was about 10⁻⁵ Hz^-1/2. On the other hand, for such power level the similar ratio determined by the fundamental photonic noise is to be about 2*10⁻⁷ Hz^-1/2. The comparison of these two values indicates that the detected noise is about 50 times larger than the expected photonic quantum noise, i.e. the real noise is determined by some other reasons.

In the interferometric detection configurations the output signals are usually observed in the presence of a significant average level of the detected light power, as a result, their sensitivity is determined by the noise of the detected laser wave rather than the electronic noise of the detection configuration. Direct measurement of the intensity noise (i.e. of the random fluctuations of the laser output power) of the DFB semiconductor laser used in our EDF based interferometric arrangement have shown that, at typical detected average light powers (< 1mW) it is comparable with the fundamental photonic quantum noise and can practically be neglected. Note that the situation was quite different for the solid-state cw Nd:YAG laser utilized in the YDF based configuration – the intensity noise was nearly two orders of magnitude larger than the estimated photonic noise.

The phase noise (i.e. that associated with random fluctuations of the phase or frequency of the laser output radiation) proved to be, however, significantly stronger in the DFB semiconductor laser. As itself, it is not detected by the photodiode, but any interferometric configuration, where there is some significant difference in the optical paths of the interfering waves, transforms the random phase/frequency fluctuations into the detected intensity noise. In particular, the intensity fluctuations resulted from the interference of two waves generated by our DFB laser and delayed by 3 m proved to be two orders of magnitude stronger than the evaluated photonic noise at the average detected power level typical for our experiments.

For such conditions, one can expect that the sensitivity of the EDF based configuration is governed by the phase noise of the DFB semiconductor laser. However, as it as mentioned above, all precautions were taken to reduce its transformation into the intensity fluctuations detected by the photodiodes. The main obvious measure was minimization of all possible reflections of the propagating light waves inside the Sagnac loop – Fig. 2(a). For this reason, all the elements of our fiber configuration were spliced and all fiber ends connected to the photodiodes were terminated with the APC connectors.

There is however, one important light reflection inside our Sagnac loop configuration which we cannot eliminate completely, and this is the reflection (i.e., the Bragg diffraction) from the recorded dynamic grating which is, obviously, necessary for operation of our adaptive interferometric arrangement. To reduce transformation of the laser phase noise into the detected light power fluctuations one can try to minimize the optical path difference between the two waves (the transmitted through the grating and the reflected from it) interfering at the photodiode. Clearly, this can be done in the best way in a completely symmetric configuration, when the recorded dynamic grating is centered in the middle of the Sagnac loop. In fact, for this reason, the doped fiber segment was put between two output tails of the fiber coupler of the same length.

The symmetry of the grating is not determined, however, by the geometry of configuration only. Indeed, the two recording waves have significantly different powers at the opposite ends of the erbium-doped fiber. Because of the light attenuation inside the doped fiber, an effective center of the grating, proves to be shifted to the end of the fiber with the higher input power. And this condition is important: indeed, the two powers are equal to each other only in case of the 50/50 coupler. But there is no average light power transmitted through the Sagnac loop in this case (see Fig. 1(b)), and the two-wave signal due to energy exchange between the transmitted and the reflected waves via the un-shifted phase grating cannot be observed, in principle.

There is also another inherent optical noise source in this configuration, and this the incoherent fluorescence because of spontaneous depopulation of the meta-stable level. In fact, the optimal conditions of the population grating are observed when the incident light power is close to the saturation power of the fiber and the meta-stable level is significantly populated. Note that the degree of population (and the fluorescence intensity) can depend strongly for the operation wavelength. Indeed the inversion of the two-level system can be close to a complete for the wavelength from the short-wavelength region 1460-1480 nm, which is utilized for optical pumping of EDFs.

Our direct measurements demonstrated that under typical conditions of the interferometer operation the fluorescence power reached ≈30% of the average signal/laser power detected in the transmitted wave. Under such conditions, the ratio between the detected effective optical noise power density and the signal power can be evaluated as $2 \sqrt{0.3 \frac{1}{Δ ν}} \approx 1.4 * 10^{- 6} H z^{- 1 / 2}$ (where $Δ ν \approx 6 * 10^{12} H z$ is an effective band of emission spectrum in EDF) that is nearly ten times higher than similar ratio for the fundamental photonic noise.

One can see that coherent interaction of the spontaneous emission with the detected average coherent signal wave can also contribute significantly to the reduction of the configuration sensitivity. We believe, however, that optimization of the configuration and reduction of the internal reflection can improve the performance of the detection configuration.

5. Conclusion

Summarizing, we have proposed the Sagnac fiber interferometer with the dynamic population grating formed in the rare-earth doped fiber for homodyne adaptive detection of an optical phase modulation. This configuration is simple, does not need active stabilization of the operation point, have a linear response, and is suitable for homodyne interferometric detection of vibrations, acoustic signals, thermo-optic effect etc. Experimentally we have demonstrated the erbium-fiber based Sagnac configuration (with the operation wavelengths 1485 nm) of the fiber accelerometers with the sensitivity which is governed basically by the phase noise of the utilized DFB semiconductor laser and by spontaneous fluorescence in the doped fiber.

References and links

1. S. J. Frisken, “Transient Bragg reflection gratings in erbium-doped fiber amplifiers,” Opt. Lett. 17(24), 1776–1778 (1992). [CrossRef] [PubMed]

2. S. Stepanov, “Dynamic population gratings in rare-earth doped optical fibers,”J. of Phys. D: Appl. Phys . 41, 224002/1–23, (2008).

3. M. D. Feuer, “Length and power dependence of self-adjusting optical fiber filters,” IEEE Photon. Technol. Lett. 10(11), 1587–1589 (1998). [CrossRef]

4. S. A. Havstad, B. Fischer, A. E. Willner, and M. G. Wickham, “Loop-mirror filters based on saturable-gain or-absorber gratings,” Opt. Lett. 24(21), 1466–1468 (1999). [CrossRef] [PubMed]

5. M. Horowitz, R. Daisy, B. Fischer, and J. L. Zyskind, “Linewidth-narrowing mechanism in lasers by nonlinear wave mixing,” Opt. Lett. 19(18), 1406–1408 (1994). [CrossRef] [PubMed]

6. Y. Cheng, J. T. Kringlebotn, W. H. Loh, R. I. Laming, and D. N. Payne, “Stable single-frequency traveling-wave fiber loop laser with integral saturable-absorber-based tracking narrow-band filter,” Opt. Lett. 20(8), 875–877 (1995). [CrossRef] [PubMed]

7. H.-C. Chien, C.-H. Yeh, C.-C. Lee, and S. Chi, “A tunable and single-frequency S-band erbium fiber laser with saturable absorber-based autotracking filter,” Opt. Commun. 250(1-3), 163–167 (2005). [CrossRef]

8. S. Stepanov, F. P. Cota, A. N. Quintero, and P. R. Montero, “Population gratings in rare-earth doped fibers for adaptive detection of laser induced ultra-sound,” J. of Holography and Speckle 5(3), 303–309 (2009). [CrossRef]

9. S. I. Stepanov, “Adaptive interferometry: A new area of applications of photorefractive crystals” in International trends in Optics, ed. by J.Goodman (Academic, Boston, 1991), 125–140.

10. A. A. Kamshilin, V. R. Romashko, and N. Y. Kulchin, “Adaptive interferometry with photorefractive crystals,” J. Appl. Phys. 105(3), 031101 (2009). [CrossRef]

11. J. W. Wagner and J. B. Spicer, “Theoretical noise-limited sensitivity of classical interferometry,” JOSA B 4(8), 1316–1326 (1987). [CrossRef]

12. D. B. Mortimore, “Fiber loop reflectors,” J. Lightwave Technol. 6(7), 1217–1224 (1988). [CrossRef]

13. S. Stepanov, E. Hernández, and M. Plata, “Two-wave mixing by means of dynamic Bragg gratings recorded by saturation of absorption in erbium-doped fibers,” Opt. Lett. 29(12), 1327–1329 (2004). [CrossRef] [PubMed]

14. S. Stepanov and E. H. Hernández, “Phase contribution to dynamic gratings recorded in Er-doped fiber with saturable absorption,” Opt. Commun. 271(1), 91–95 (2007). [CrossRef]

15. S. Stepanov and C. Nuñez Santiago, “Intensity dependence of the transient two-wave mixing by population grating in Er-doped fiber,” Opt. Commun. 264(1), 105–115 (2006). [CrossRef]

16. A. V. Tveten, A. Dandridge, C. M. Davis, and T. G. Giallorenzi, “Fibre optic accelerometer,” Electron. Lett. 16(22), 854–856 (1980). [CrossRef]

17. P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers: Fundamentals and Technology (Academic, 1999).

18. S. Stepanov, A. Fotiadi, and P. Mégret, “Effective recording of dynamic phase gratings in Yb-doped fibers with saturable absorption at 1064nm,” Opt. Express 15(14), 8832–8837 (2007). [CrossRef] [PubMed]

Adaptive Sagnac interferometer with dynamic population grating in saturable rare-earth-doped fiber

Abstract

1. Introduction

2. Operation principle

3. Experimental results

4. Discussion

5. Conclusion

References and links

Cited By

Figures (7)

Equations (9)

Optics Express